Tree ensembles can also be trained using the boosting technique [1]}, [2]}, [3]}
in order to yield boosted trees, which are multi-sets of the form
\(B = \lbrace \langle T_1, \alpha _1\rangle , \ldots , \langle T_m, \alpha _m\rangle \rbrace \) ,
where each \(T_i \, (i \in [m])\)  is a decision tree and \(\mathbf {\alpha }\)  is a convex combination of coefficients.In other words, \(\alpha _i \ge 0\)  for all \(i \in [m]\)  and \(\sum _i \alpha _i = 1\) .
By analogy with random forests, the decisions made by boosted trees are given from a weighted majority vote:
\(B(\mathbf {x}) ={\left\lbrace \begin{array}{ll}1 & \mbox{ if } \sum _{i=1}^m \alpha _i T_i(\mathbf {x}) > \frac{1}{2} \\0 & \mbox{ otherwise.}\end{array}\right.}\) 
